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X = BC = 2

Blue Area = 13.2548339959

Blue Area = 7.06858347058

X = BC = BM = AM = 3

Simplified / Improved

X = AM = BM = BC = DM = 3

X / R = 1.41421356237

Shaded Fraction = 1 / 9

Max Shaded Fraction ( Easy Way )

Max Shaded Fraction ( Improved )

Shaded Area = 30 Square Units

X = R ( 2 / √ 2 - 1 )